Self-calibrating oversampling electromechanical modulator and self-calibration method

ABSTRACT

An oversampling electromechanical modulator, including a micro-electromechanical sensor which has a first sensing capacitance and a second sensing capacitance and supplies an analog quantity correlated to the first sensing capacitance and to the second sensing capacitance; a converter stage, which supplies a first numeric signal and a second numeric signal that are correlated to the analog quantity; and a first feedback control circuit for controlling the micro-electromechanical sensor, which supplies an electrical actuation quantity correlated to the second numeric signal. The electromechanical modulator moreover includes a second feedback control circuit for calibrating the micro-electromechanical sensor, which includes an offset-sensing circuit that can be activated by the first numeric signal, and a programmable calibration circuit, having a programmable calibration capacitance, which is connected to the micro-electromechanical sensor and is controlled by the offset-sensing circuit for balancing of the first sensing capacitance and second sensing capacitance.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional of U.S. patent application Ser. No.10/198,720, filed Jul. 16, 2002, now pending, which application isincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a self-calibrating oversamplingelectromechanical modulator and to a self-calibration method.

2. Description of the Related Art

As is known, the use of micro-electromechanical-system (MEMS) sensorswith differential capacitive unbalance has been proposed for building,for example, linear or rotational accelerometers and pressure sensors.

In particular, MEMS sensors of the above-mentioned type comprise a fixedbody (stator) and a mobile mass, which are generally of an appropriatelydoped semiconductor material, are connected together byelastic-suspension elements (springs) and are constrained in such a waythat the mobile mass has, with respect to the stator, predetermineddegrees of freedom, which are translational and/or rotational. Inaddition, the stator and the mobile mass have a plurality of fixed armsand of mobile arms, respectively, in a comb-finger arrangement. Inpractice, each mobile arm is arranged between a pair of fixed arms, soas to form a pair of capacitors which have a common terminal and acapacitance that depends upon the relative positions of the arms, namelyupon the position of the mobile mass with respect to the stator (sensingcapacitance). The fixed arms are then connected to external sensingterminals. When a sensor is excited, its mobile mass is displaced andthere is an unbalance between the capacitances of the capacitors, whichcan be detected at the sensing terminals.

In addition, MEMS sensors are equipped with actuation capacitors, whichare provided between the stator and the mobile mass and are connected toexternal actuation terminals. When a voltage is supplied on saidactuation terminals, between the plates of the actuation capacitors anelectrostatic actuation force is exerted (in all cases of an attractivetype), which displaces the mobile mass with respect to the stator. Theactuation terminals may even coincide with the sensing terminals.

MEMS sensors are normally associated to electronic read and controlcomponents, with which they form oversampling electromechanicalmodulators.

For greater clarity, reference may be made to FIG. 1, which shows anoversampling electromechanical modulator 1 comprising a MEMS sensor 2,for example a linear-type accelerometer, a charge integrator 3, aone-bit quantizer 4, and a feedback actuator 5, which are connectedtogether so as to form a control loop. In greater detail, the MEMSsensor 2, the charge integrator 3 and the quantizer 4 form the forwardpath of the control loop, while the feedback actuator 5, which isconnected between an output of the quantizer 4 and an actuation input 2a of the MEMS sensor 2, forms the feedback line.

The MEMS sensor 2 is connected to the charge integrator 3, which, in asensing step, detects the capacitive unbalance of the sensor 2 andsupplies, on an output—which is connected to an input of the quantizer4, an analog signal V_(M) correlated to said capacitive unbalance. Thequantizer 4 generates at its output a bitstream BS, in which each bitrepresents the sign of the analog signal V_(M) at a respective samplinginstant.

The feedback actuator 5 receives at input the bitstream BS and, in anactuation step following upon the sensing step, supplies to theactuation input 2 a of the MEMS sensor 2 a feedback-actuation voltageV_(FB) for counteracting the displacement of the mobile mass of the MEMSsensor 2 and bringing the mobile mass back into the resting position.

In an ideal MEMS sensor, when no external stress are present and novoltages are applied to the actuation terminals, the mobile arms shouldbe exactly in an intermediate position between the respective fixed armsthat are arranged facing them, and the capacitances should be balanced.This means that in an ideal electromechanical modulator the mobile massof the MEMS sensor should oscillate about the nominal resting position,and the bitstream BS should have a zero average (namely, the bitstreamBS should be formed by a sequence of bits having alternating logicvalues, such as +1 −1 +1 −1, etc.).

In actual fact, notwithstanding the extremely high precision of themicromachining techniques used for building MEMS sensors, it isunavoidable that the mobile mass is affected by a position offset;consequently, also in resting conditions the mobile arms are notequidistant from the fixed arms. As a result, MEMS sensors have anintrinsic capacitive unbalance which, in an electromechanical modulator,causes an offset of the bitstream BS (in practice, the average of thebitstream BS is not zero).

At present, in order to correct the offset of electromechanicalmodulators, an in-factory calibration process is carried out, whichinvolves various steps and which will be briefly described withreference to FIG. 2. In addition to illustrating the electromechanicalmodulator 1, FIG. 2 also shows a measurement-interface circuit 7 and acalibration circuit 8. In particular, the calibration circuit 8 isprogrammable and supplies a calibration voltage V_(CAL) to a calibrationterminal 2 b of the MEMS sensor 2 in order to exert an electrostaticforce on the mobile mass of the MEMS sensor 2 itself.

First of all, the electromechanical modulator 1 is set in a quiescentstate, in which the MEMS sensor 2 does not undergo any stress, and thefeedback loop is opened by disconnecting the feedback actuator 5 fromthe actuation terminal 2 a of the MEMS sensor 2.

Next, the measurement-interface circuit 7 is connected to the input ofthe quantizer 4 and detects the value of the analog signal V_(M), which,in the conditions described, is due exclusively to the position offsetof the mobile mass of the MEMS sensor 2. In particular, themeasurement-interface circuit 7 generates an offset signal V_(OFF)correlated to the analog signal V_(M.)

Next, the calibration circuit 8 is programmed by causing the calibrationvoltage V_(CAL) to vary until the offset signal V_(OFF) is minimized andthe mobile mass of the MEMS sensor 2 is brought back into the proximityof the nominal resting position.

Subsequently, if the sensing capacitances present between the mobilemass and the stator of the MEMS sensor 2 are unbalanced, the calibrationis completed by connecting one or more calibration capacitors 9 inparallel to the smaller sensing capacitance.

The devices according to the prior art have some drawbacks. In the firstplace, calibration can be performed only in the factory, andconsequently it cannot be ensured that the precision will remainunaltered over time. In fact, the mechanical properties of a MEMSsensor, especially as regards the elastic-suspension elements, areaffected by environmental conditions (for instance, by the temperature)and in any case vary on account of the ageing of the MEMS sensor itself.In practice, the initial calibration is lost and an offset arises again.

In addition, MEMS sensors are extremely sensitive and are able to detecteven minimal vibrations. Consequently, it is very difficult to create acondition of effective absence of stress in which a precise calibrationcan be performed.

BRIEF SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a self-calibratingelectromechanical modulator and a corresponding self-calibration methodthat will enable the above-mentioned drawbacks to be overcome.

According to the present invention, an oversampling self-calibratingelectromechanical modular and a corresponding self-calibration methodare provided.

According to an embodiment of the invention, an oversamplingelectromechanical modulator is provided, including amicro-electromechanical sensor which has a first sensing capacitance anda second sensing capacitance and supplies an analog quantity correlatedto the first sensing capacitance and to the second sensing capacitance;a converter stage, which supplies a first numeric signal and a secondnumeric signal that are correlated to the analog quantity; and a firstfeedback control circuit for controlling the micro-electromechanicalsensor, which supplies an electrical actuation quantity correlated tothe second numeric signal. The electromechanical modulator moreoverincludes a second feedback control circuit for calibrating themicro-electromechanical sensor, which includes an offset-sensing circuitthat can be activated by the first numeric signal, and a programmablecalibration circuit, having a programmable calibration capacitance,which is connected to the micro-electromechanical sensor and iscontrolled by the offset-sensing circuit for balancing of the firstsensing capacitance and second sensing capacitance.

According to another embodiment of the invention, a method forcalibrating an oversampling electromechanical modulator is provided, inwhich the modulator includes a micro-electromechanical sensor having astator body and a mobile mass, between which there are a first sensingcapacitance and a second sensing capacitance.

The method includes the steps of supplying a first analog quantitycorrelated to the first sensing capacitance and to the second sensingcapacitance and generating a first numeric signal correlated to saidanalog quantity. The method further includes connecting, to saidmicro-electromechanical sensor, a programmable-calibration circuithaving a programmable calibration capacitance and modifying theprogrammable calibration capacitance in the presence of a continuouscomponent of the numeric signal.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

For a better understanding of the present invention, an embodimentthereof is now described, purely by way of non-limiting example, withreference to the attached drawings, in which:

FIG. 1 is a simplified block diagram of an oversamplingelectromechanical modulator of a known type;

FIG. 2 is a block diagram of the modulator of FIG. 1 in a calibrationstep;

FIG. 3 is a simplified block diagram of an oversamplingelectromechanical modulator according to the present invention;

FIG. 4 is a simplified perspective view of a micro-electromechanicalsensor of the electromechanical modulator of FIG. 3;

FIGS. 5, 6A-6H, 7A, and 7B show plots in time of quantities related tothe electromechanical modulator of FIG. 3; and

FIG. 8 is a circuit diagram of a block of the diagram of FIG. 3.

DETAILED DESCRIPTION OF THE INVENTION

The invention finds advantageous application in all cases in which amicro-electromechanical sensor is used for detecting a quantity thefrequency spectrum of which does not include the continuous component(i.e., it does not comprise a zero frequency). For example, anelectromechanical modulator according to the present invention can beused for controlling the position of R/W heads for reading and writinghard disks in electronic computers.

With reference to FIG. 3, an oversampling electromechanical modulator 10comprises a MEMS sensor 11, a converter stage 12, a feedback stage 13,an offset-sensing stage 14, and a calibration circuit 15.

The MEMS sensor 11, the structure of which is shown in FIG. 4, in theembodiment herein described is a linear accelerometer for detection ofan acceleration A and comprises a stator 100 and a mobile mass 101. Thestator 100 and mobile mass 101, which are made of an appropriately dopedsemiconductor material, are connected together by means ofelastic-suspension elements (springs) 102 and are constrained in such away that the mobile mass 101 has a translational degree of freedom withrespect to the stator 100. In addition, the stator and the mobile masshave a plurality of fixed arms 104 and a plurality of mobile arms 105,respectively, which are comb-fingered together. In practice, each mobilearm 105 is arranged between a pair of fixed arms 104, so as to form apair of capacitors which have a common terminal and a capacitance thatdepends upon the relative positions of the arms, namely upon theposition of the mobile mass with respect to the stator.

Again with reference to FIG. 3, the MEMS sensor 11 is here schematicallyrepresented by a first sensing capacitor 17 and a second sensingcapacitor 18, which respectively have a first sensing capacitanceC_(S1), and a second sensing capacitance C_(S2). In particular, thefirst sensing capacitor 17 is connected between a first stator terminal21 and a common terminal 20, which is connected to the mobile mass 101of the MEMS sensor 11, and the second sensing capacitor 18 is connectedbetween a second stator terminal 22 and the common terminal 20.

The converter stage 12 comprises a charge integrator 24, a quantizer 25,a correction circuit 26, a decimator 27, and an IIR filter 28, which arecascaded together.

In greater detail, the charge integrator 24 has a pair of inputs, one ofwhich is connected to the first stator terminal 21 and the other to thesecond stator terminal 22 of the MEMS sensor 11, and an output 24 awhich is connected to an input of the quantizer 25 and supplies ananalog voltage V_(M) correlated to the capacitive unbalance between thestator terminals 21, 22.

The quantizer 25, which in the present case is a one-bit quantizer, hasan output connected to a signal input 26 a of the correction circuit 26and supplies a quantization bitstream BS_(Q), the bits of which arecorrelated to the signal of the capacitive unbalance between the statorterminals 21, 22 with respect to the common terminal 20. Thequantization circuit 26 moreover has a control input 26 b, which isconnected to the feedback stage 13, as will be explained in greaterdetail hereinafter, and an output 26 c which supplies an outputbitstream BS_(O) and is connected to an input of the decimator 27, whichin turn is cascaded to the IIR filter 28.

The IIR filter 28 has an output 28 a forming the output of the modulator10 and supplying a numeric signal X_(K) that represents the accelerationA to which the MEMS sensor 11 is subjected in a generic sampling instantK.

The feedback stage 13 comprises a damping-control circuit 30, a feedbackcompensator 31, and an actuation-control circuit 32.

In detail, the damping-control circuit 30 has a first input 30 a, whichis connected to the output 26 a of the quantizer 25 and receives thequantization bitstream BS_(Q), and a second input 30 b, which isconnected to the offset-sensing stage 14, as will be explained later on.In addition, the damping-control circuit 30 has a first output 30 c,which is connected to a first input of the actuation-control circuit 32and to the control input 26 b of the correction circuit 26 and suppliesa first feedback-control signal FB_(C); a second output 30 d, which isconnected to a second input of the actuation-control circuit 32 andsupplies a second feedback-control signal FB_(H); and a third output 30e, which is connected to an input of the feedback compensator 31 andsupplies a feedback bitstream BS_(FB).

The feedback compensator 31 has an output 31 a that supplies acompensation bitstream BS_(COMP) and is connected to a first input of afirst selector 34. The first selector 34 has also a second inputconnected to the third output 30 e of the damping-control circuit 30, soas to receive the feedback bitstream BS_(FB); a control input connectedto the first output 30 c of the damping-control circuit 30, so as toreceive the first feedback-control signal FB_(C); and an output 34 awhich is connected to a third input of the actuation-control circuit 32.

The actuation-control circuit 32 comprises a multiplexer 33, a secondselector 35, and at least a first voltage generator 36 a and a secondvoltage generator 36 b, respectively supplying a first voltage V₁ and asecond voltage V₂ which are distinct from one another (for instance, thesecond voltage V₂ is higher than the first voltage V₁). In detail, themultiplexer 33 has a first control terminal and a second controlterminal which are respectively connected to the first output 30 c andto the second output 30 d of the damping-control circuit 30; a firsttransfer terminal and a second transfer terminal which are respectivelyconnected to the first voltage generator 36 a and to the second voltagegenerator 36 b; and an output 33 a, which is connected to an input ofthe second selector 35 and supplies an actuation voltage V_(A). Inparticular, during the self-calibration steps, the actuation voltageV_(A) is equal to the second voltage V₂ when both the firstfeedback-control signal FB_(C) and the second feedback-control signalFB_(H) are high; otherwise, it is equal to the first voltage V₁. Duringnormal operation of the device, instead, the actuation voltage V_(A) isset equal to the second voltage V₂ whenever a change of sign is detectedin the feedback bitstream BS_(FB); immediately afterwards, the actuationvoltage V_(A) is brought back again to the value of the first voltageV₁.

The second selector 35 has a control terminal, which is connected to theoutput 34 a of the first selector 34, and a first output and a secondoutput, which are respectively connected to the first stator terminal 21and to the second stator terminal 22 of the MEMS sensor 11.

In this way, in practice, the stator terminals 21, 22 are used also asactuation terminals (with time-sharing access), and it is possible toexert on the mobile mass 101 of the MEMS sensor 11 electrostaticfeedback forces which are different also in absolute value, besidesbeing different in direction. The absolute value is in fact determinedby the value of the actuation voltage V_(A), whereas the directiondepends upon whether the actuation voltage V_(A), via the secondselector 35, is supplied to the first stator terminal 21 or to thesecond stator terminal 22. In practice, when the actuation voltage isequal to the second voltage V₂, a force having higher absolute value isexerted.

The offset-sensing stage 14 comprises a low-pass filter 37, a comparatorcircuit 38, and an offset-compensation circuit 39.

In detail, the low-pass filter 37, which has a cutoff frequencypreferably lower than 30 Hz, has an input connected to the output 28 aof the IIR filter 28 and an output 37 a connected to inputs of thecomparator circuit 38 and of the offset-compensation circuit 39 andsupplying a filtered signal X_(F), which indicates the continuouscomponent of the numeric signal X_(K).

The comparator circuit 38 moreover has an output which is connected tothe offset-compensation circuit 39 and to the second input 30 b of thedamping-control circuit 30 and supplies an enabling signal EN. Inparticular, the enabling signal EN has a first logic value (for examplehigh) when the filtered signal X_(F) is higher than a predeterminedthreshold, and a second logic value (low) otherwise; in addition, thesaid threshold is preferably programmable, in a way in itself known.

The offset-compensation circuit 39 has an output 39 a connected to thecalibration circuit 15 and supplies a calibration signal CAL, whichindicates the value of a calibration capacitance to be connected to theMEMS sensor 11 for compensating the presence of possible offsets, asexplained hereinafter.

The calibration circuit 15 comprises an N-bit register 40 (for example,with N=7) and a programmable capacitive network 41.

The register 40 has a writing input connected to the output 39 a of theoffset-compensation circuit 39, in such a way as to receive thecalibration signal CAL; programming outputs 40.1, . . . , 40.N−1, whichare connected to respective programming inputs of the programmablecapacitive network 41 and supply respective programming signalsB₁-B_(N−1); and a sign output 40.N, which supplies a sign bit B_(N).

The programmable capacitive network 41 (an embodiment of which is shownin FIG. 8) is selectively connectable in parallel to the first sensingcapacitor 17 or to the second sensing capacitor 18. In greater detail,the programmable capacitive network 41 has a first terminal connected tothe common terminal 20 of the MEMS sensor 11 and a second terminalconnected to an input 43 a of a third selector 43, which moreover has acontrol terminal connected to the sign output 40.N of the register 40.The third selector 43 also has a first output and a second output whichare respectively connected to the first stator terminal 21 and to thesecond stator terminal 22 of the MEMS sensor 11. In addition, theprogrammable capacitive network 41 has a calibration capacitance C_(CAL)ranging between a minimum value and a maximum value (for example, 0.45fF and 28.8 fF, respectively) with discrete step increments ΔC_(CAL),for example 0.45 fF. In other words, the calibration capacitance C_(CAL)may assume a predetermined number of discrete values comprised betweenthe maximum value and the minimum value, and the step ΔC_(CAL)represents the unit increment between any two successive values.

Operation of the oversampling modulator 10 will be describedhereinafter.

The electromechanical modulator 10 is timed in a known way and has clockcycles with a predetermined duration.

In normal operating conditions, i.e., when the capacitances C_(S1),C_(S2) of the sensing capacitors 17,18 are balanced at rest, thecontinuous component of the numeric signal X_(K) is substantiallyabsent, given that the band of the quantity detected by the MEMS sensor11 (acceleration A) does not comprise zero frequency.

In this case, the filtered signal X_(F) generated by the low-pass filter37 is lower than the threshold of the comparator 38, the enabling signalEN is low, and the offset-compensation circuit 39, which is disabled,holds the calibration signal CAL on the output 39 a at a zero value. Inaddition, when the enabling signal EN is low, the damping-controlcircuit 30 sets the feedback-control signals FB_(C), FB_(H) at a firstlogic value, for example low. In this condition, the feedback bitstreamBS_(FB) and the output bitstream BS_(O) are equal to the quantizedbitstream BS_(Q), which substantially has a zero average, and, moreover,the feedback selector 34 connects its own output 34 a to the output 31 aof the feedback compensator 31. According to the pattern of the feedbackbitstream BS_(FB), the actuation-control circuit 32 selects one of thevalues of the actuation voltage V_(A) and supplies it selectively to oneof the stator terminals 21, 22 of the MEMS sensor 11, in a way in itselfknow and described, for example, in “A Fully Differential Lateral ΣΔAccelerometer with Drift Cancellation Circuitry,” by M. A. Lemkin, B. E.Boser, and D. M. Auslander, Solid-State Sensor and Actuator Workshop,Hilton Head, S.C. , 1996. In practice, the electromechanical modulator11 implements an analog-to-digital converter substantially of thesigma-delta type. It should, however, be pointed out that oversamplingelectromechanical modulators present certain peculiarities whereby theycannot be strictly accommodated within the category of sigma-deltaconverters, as is known and as is explained in the above-mentionedarticle.

If, instead, the capacitances between the stator terminals 21, 22 andthe common terminal 20 are not balanced at rest, in the band of thenumeric signal X_(K) there is a non-zero continuous component.Consequently, the filtered signal X_(F) is different from zero and, ifit exceeds the threshold of the comparator 38, activates aself-calibration step. In particular, the enabling signal EN switches,going to the high state, and activates the offset-compensation circuit39, which, using the filtered signal X_(F), determines a value of thecalibration signal CAL. The calibration signal CAL, which is nownon-zero, is then used to modify the contents of the register 40 and,consequently, the value of the calibration capacitance C_(CAL) of theprogrammable capacitive network 41. In particular, the calibrationsignal CAL alternatively determines either an increase or a decrease byone step ΔC_(CAL) of the calibration capacitance C_(CAL), according tothe sign of the filtered signal X_(F). In addition, the value of thesign bit B_(N) supplied by the sign output 40.N of the register 41controls the third selector 43 in such a way as to connect theprogrammable capacitive network 41 in parallel to one between firststator capacitor 17 and the second stator capacitor 18, in particular tothe one having smaller capacitance.

According to the invention, in practice, the converter stage 12, theoffset-sensing stage 14, and the calibration circuit 15 form, with theMEMS sensor 11, a calibration-control loop. In this way, it is possibleto automatically detect and eliminate the effects due to positionoffsets of the mobile mass 101 or to any intrinsic capacitive unbalanceof the MEMS sensor 11, which give rise to a continuous component of thenumeric signal X_(K). In fact, whenever the filtered signal X_(F)exceeds the threshold of the comparator 38, a calibration step isactivated, during which the value of the calibration capacitance C_(CAL)is varied by one step ΔC_(CAL), so as to re-balance the capacitancesC_(S1), C_(S2) of the stator capacitors 17, 18. Since the phenomena thatcause drifts and the appearance of offsets in MEMS sensors are slow ifcompared to the variations in the electrical operating quantities, asingle calibration step is generally sufficient for eliminating thecontinuous component of the numeric signal X_(K). Otherwise, at the endof the first calibration step, a residual continuous component in theband of the numeric signal X_(K) is again detected automatically, and anew calibration step is carried out iteratively.

The electromechanical modulator 10 operates also to reduce themechanical stress on the MEMS sensor 11 and the distortions of thenumeric signal X_(K) which occur during a settling transient of theself-calibration step, in particular on account of the variationsimposed on the calibration capacitance C_(CAL) of the programmablecapacitive network 41. As is known, in fact, these variations modify theaverage electrostatic forces applied to the mobile mass 101 of the MEMSsensor 11, which thus stabilizes itself, with damped oscillations, abouta new mean position of equilibrium X_(E) (see, in this connection, FIG.5, in which the instant at which the calibration capacitance C_(CAL) ismodified is designated by T₀, and the duration of the settling transientis designated by T_(TR)).

In detail, when the filtered signal X_(F) exceeds the threshold of thecomparator 38 (instant T₀), the enabling signal EN is set at the highstate and enables the offset-compensation circuit 39, as alreadyexplained. In addition, when the enabling signal EN is high, thedamping-control circuit 30 sets the first feedback-control signal FB_(C)at a second logic value (high), whilst the second feedback-controlsignal FB_(H) remains low. In this way, the first selector 34 switchesand connects its own output 35 a with the third output 30 e of thedamping-control circuit 30, in practice de-activating the feedbackcompensator 31. In addition, the multiplexer 33 sets the actuationvoltage V_(A) equal to the first voltage V₁ (FIG. 6D).

With reference also to FIGS. 6A-6H, starting from the instant T₀, thedamping-control circuit 30 modifies the feedback bitstream BS_(FB) inthe way that is described in what follows. Initially and up to aninstant T₁, in which the analog voltage V_(M) changes sign for the firsttime (FIG. 6B), the feedback bitstream BS_(FB) remains at one and thesame constant value (FIG. 6C). in this step, the actuation voltage V_(A)is equal to the first voltage V₁, and an electrostatic force constant inabsolute value and in direction is applied to the mobile mass 101 of theMEMS sensor 11 in such a way as to displace the mobile mass 101 itselftowards the new position of equilibrium X_(E) (FIGS. 6D and 6E). Inaddition, when, at the instant T₀, the first feedback-control signalFB_(C) switches going to the high state, the correction circuit 26modifies the output bitstream BS_(O) and supplies a bitstream with zeroaverage (+1 −1 +1 −1, etc.).

At the instant T₁, the feedback bitstream BS_(FB) switches, and thedamping-control circuit 30 sets the second feedback-control signalFB_(H) at the high state (FIG. 6G). Consequently, the actuation voltageV_(A) is now equal to the second voltage V₂. In addition, theelectrostatic force F changes direction and has a magnitude greater thanin the time interval comprised between the instants T₀ and T₁(FIGS. 6Dand 6E).

Next, while in a clock cycle immediately following upon the instant T₁the feedback-control signals FB_(C), FB_(H) are brought back to the lowvalue (FIGS. 6F and 6G), the feedback bitstream BS_(FB) is kept constantfor a predetermined number M of clock cycles. At this point, thedamping-control circuit 30 and the correction circuit 26 return to thenormal operating conditions, and the feedback bitstream BS_(FB) andoutput bitstream BS_(O) are again set equal to the quantizationbitstream BS_(Q). In addition, the enabling signal EN switches andreturns to the low state.

Since a residual high-frequency noise is superimposed on the analogsignal V_(M), the instant T₁ at which for the first time after theinstant T₀ the analog signal V_(M) changes sign (and the feedbackbitstream BS_(FB) switches) precedes the instant T₂ at which the mobilemass 101 of the MEMS sensor 11 reaches the new position of equilibriumX_(E) (FIG. 6A). In practice, in order to prevent, in the movement ofthe mobile mass 101, extreme over-elongations beyond the new position ofequilibrium X_(E), the mobile mass 101 is initially decelerated with afirst electrostatic force F pulse opposite to the direction of motionand having high magnitude, and next with M pulses which are all in thesame direction as the first pulse, but have a smaller magnitude. Inaddition, the first pulse is supplied in advance with respect to theinstant T₂ at which the mobile mass 101 of the MEMS sensor 11 reachesthe new position of equilibrium X_(E), and the M subsequent pulses areall in the same direction, irrespective of the changes in sign of theanalog signal V_(M), and hence of the quantization bitstream BS_(Q).

At the same time, the action of the correction circuit 26, whichsupplies a zero-average bitstream during the self-calibration step,makes it possible to prevent disturbance peaks of the numeric signalX_(K) due to the transient unbalancing induced into theelectromechanical modulator 10 precisely for carrying outself-calibration. By way of example, FIGS. 7 a and 7 b show the plot ofthe numeric signal X_(K) in response to a same input waveform. In bothcases, a self-calibration step is performed, but in the example of FIG.7A the correction circuit 26 has been deactivated (the arrows identifystart of the self-calibration step).

With reference to FIG. 8, the programmable capacitive network 41preferably comprises a battery of insertable capacitors 45 and a fixedcapacitive network 46 which has a predetermined capacitance and has afirst terminal connected to the input 43 a of the third selector 43, anda second terminal 46 a. Each of the insertable capacitors 45 has a firstterminal connected to the second terminal 46 a of the fixed capacitivenetwork 46 and a second terminal alternatively connectable to ground andto the common terminal 20 of the MEMS sensor 11 via a respectiveprogramming selector 47. The programming selectors 47 moreover havecontrol terminals connected to a respective one among the programmingoutputs 40.1, . . . , 40.N−1 of the register 40 and are each controlledby a respective programming bit B₁-B_(N−1).

The insertable capacitors 45 have respective binarily weightedcapacitances, namely capacitances respectively equal to C₀, 2C₀, . . . ,2_(N−1)C₀. In practice, the whole capacitance between the secondterminal 46 a of the fixed capacitive network 46 and the common terminal20 is equal to the sum of the capacitances of the insertable capacitors45 that are actually used and can range from C₀ to (2^(N)−1)C₀.

It is clear from the above discussion that the electromechanicalmodulator according to the present invention affords the followingadvantages. In the first place, it is possible to detect and correctautomatically any offsets that may arise during use of the device, andhence after the preliminary calibration performed in the factory. Inaddition, self-calibration can be carried out during normal operation ofthe electromechanical modulator, and the MEMS sensor 11 does not have tobe set in any particular quiescent conditions.

A further advantage is that, during self-calibration, themicro-electromechanical structure is driven so as to avoid abruptmechanical stress, which could damage it. In particular, the maximumvalue of modification of the capacitance in the calibration step isdivided into a plurality of unit increments, and, in eachself-calibration step, the calibration capacitance C_(CAL) of theprogrammable capacitive network 41 is varied by only one unit incrementΔC_(CAL). Possibly, self-calibration can be repeated iteratively if theinitial offset is not completely eliminated. In addition, the mobilemass 101 of the MEMS sensor 11 is decelerated before the new position ofequilibrium is reached, so as to avoid extreme over-elongations.

In addition, the correction applied to the output bitstream BS_(O)enables a considerable reduction in the distortions of the numericsignal X_(K) during a self-calibration step.

Finally, it is clear that modifications and variations may be made tothe electromechanical modulator described herein, without therebydeparting from the scope of the present invention.

For example, a MEMS sensor having rotational and/or translationaldegrees of freedom other than the ones illustrated can be used. Inaddition, the actuation-control circuit 32 could supply an arbitrarynumber of values of the actuation voltage so as to be able to applyelectrostatic forces having different intensities to the mobile mass.

All of the above U.S. patents, U.S. patent application publications,U.S. patent applications, foreign patents, foreign patent applicationsand non-patent publications referred to in this specification and/orlisted in the Application Data Sheet, are incorporated herein byreference, in their entirety.

1. A method for calibrating an oversampling electromechanical modulatorwhich includes a micro-electromechanical sensor having a stator body anda mobile mass, between which there are a first sensing capacitance and asecond sensing capacitance; the method comprising the steps of:supplying a first analog quantity correlated to a difference betweensaid first sensing capacitance and said second sensing capacitance;generating a first numeric signal correlated to said analog quantity;converting said first numeric signal to an output signal; providing theoutput signal at an output of the electromechanical modulator;connecting, to said micro-electromechanical sensor; modifying saidprogrammable calibration capacitance to eliminate a steady-statecomponent of said numeric signal.
 2. The method according to claim 1wherein the modifying step comprises the steps of: generating a filteredsignal correlated to said steady-state component of said first numericsignal; and comparing said filtered signal with a predeterminedthreshold.
 3. The method according to claim 2 wherein said step ofgenerating said filtered signal comprises filtering said first numericsignal with a cutoff frequency of less than 30 Hz.
 4. The methodaccording to claim 1 wherein the modifying step moreover comprisesvarying said programmable calibration capacitance by a predeterminedamount.
 5. The method according to claim 1 wherein the modifying step isfollowed by the step of damping any oscillations of said mobile mass ofsaid micro-electromechanical sensor during a settling transient.
 6. Themethod according to claim 5, wherein said step of damping anyoscillations comprises the steps of: supplying said mobile mass with afirst force pulse having a first magnitude and a direction opposite to adirection of motion of said mobile mass; and supplying said mobile masswith a predetermined number of second consecutive force pulses having asecond magnitude smaller than said first magnitude and having saiddirection.
 7. The method according to claim 6 wherein the step ofdamping any oscillations further comprises detecting a direction of saidanalog quantity, and in that said first force pulse is supplied at thefirst change of direction of said analog quantity during said settlingtransient.
 8. The method according to claim 6, further comprising thestep of generating an electrical actuation quantity having a firstvoltage value and a second voltage value, which is higher than saidfirst voltage value; said step of supplying a first force pulsecomprising selecting said second voltage value, and said step ofsupplying a predetermined number of second consecutive force pulsescomprising selecting said first voltage value.
 9. The method accordingto claim 1 wherein, after said modification step, a zero-average numericsignal is used for generating said first numeric signal.
 10. A methodfor calibrating an electromechanical modulator, comprising: detecting anunbalance of a sensing capacitance; generating an analog signalcorresponding to the detected unbalance; converting the analog signal toan output signal; providing the output signal at an output of theelectromechanical modulator; detecting a steady-state component of theanalog signal; modifying an existing calibration capacitance tocompensate for the detected steady-state component.
 11. The method ofclaim 10, comprising applying a damping voltage to the sensingcapacitance to reduce mechanical stress arising from the modifying. 12.The method of claim 10 wherein the detecting a steady-state componentcomprises applying a low-pass filter to the analog signal.
 13. Themethod of claim 10 wherein the detecting a steady-state componentcomprises detecting a steady-state component that exceeds a threshold.14. The method of claim 10 wherein: the detecting an unbalance comprisessupplying an analog quantity correlated to a capacitive differencebetween a first sensing capacitance and a second sensing capacitance ofa micro-electromechanical sensor; the generating comprises generating anumeric signal correlated to the analog quantity; and the modifyingcomprises modifying the existing calibration capacitance to eliminatethe steady-state component of the numeric signal.
 15. The method ofclaim 10 wherein: the detecting an unbalance comprises detecting anunbalance of a first capacitance and a second capacitance of amicro-electromechanical sensor configured to be unbalanced by physicaldisplacement of the sensor; the generating comprises providing adisplacement signal correlated to the unbalance of the first and secondcapacitances; and the modifying comprises eliminating the steady-statecomponent of the displacement signal.